Two-terminal low-pass coupling system



July 25, 1939. H. A. WHEELER TWO-TERMINAL LOW-PASS COUPLING SYSTEM FiiedApril 22, 1938 2 Sheets-Shed 1 00 Total FIG.|.

Frequency INV TOR A. WHEELER EN HA OLD ATTORNEY July 25, 1939.

Filed April 22, 1938 H. A. WHEELER TWO-TERMINAL LOW-PASS COUPLING SYSTEM2 Sheets-Sheet 2 FIG.8.

FIGJO.

IINVENTOR OLD A. vmE

ATTORNEY Patented Ju1y2 5, 1939 UNITED STATES Two-mammal. LOW-PASS commasrs'mm Harold A. Whcelen Great Neck N. Y.,, assignor to HaseltineCorporation, a corporation of Delaware Application April 22, 1938,Serial No. 203,597 10 Claims. (01. 178-44) This invention relatesgenerally to low-pass coupling systems and particularly to low-passcoupling systems including a pair of terminals in parallel with whichthere is substantial capac- 5 itance and. across which it is desired tobuild up a high impedance or admittance which is substantially constantover a wide range of frequencies.

In many low-pass coupling systems it is dem sirable to build up asubstantially uniform impedance having the highest possible mean valueover a wide range of frequencies between terminals having susceptance inparallel therewith; that is, it is desirable to maintain approximately15 the maximum mean value of impedance between the terminals over a widerange of frequencies. For example, in the design of vacuum-tubeamplifiers to pass a wide band of frequencies, it is desirable to buildup across capacitance, com prising the inherent capacitances of the tubecircuits to be coupled, the maximum impedance that can be maintainedsubstantially uniform over the operating frequency band of theamplifler, such impedance being limited by the inherent capacitances ofthe tube circuits to be coupled. Prior art coupling arrangementsutilized for this purpose have fallen far short of the desired results.

It is an object of the present invention, therefore, to provide alow-pass coupling system comprising a pair of terminals across whichthere is shunt susceptance and across which a maximum and substantiallyconstant value of impedance is maintained over a wide range offrequencies.

It is another object of the invention to provide a low-pass coupling.system having maximum impedance over a wide frequency range for usebetween two successivetubes oi a vacuum-tube amplifier.

In accordance with one embodiment of the invention, a two-terminallow-pass signal-translating system for operation over a wide range offrequencies comprises a pair of terminals common to the input and theoutput circuits of the 45 system across which there is effectivelycapacitance tending to limit the response of the system over its range.A dead-end filter having a predetermined image impedance over the rangeis coupled to the terminals, the filter comprising 5 only a part of thecapacitance across the terminals as a terminal mid-shunt element. Animpedance termination is provided coupled to the dead-end of the filterproportioned substantially to match the image impedance of the filterover its range, the reactive constants of the deadend filter being soproportioned relative to the capacitance across the terminals of theoperating frequency range that the mean value of the impedance acrossthe terminals over the range is approximately the maximum that can bemain- 6 tained'over the'range.

Other modifications and applications of the dead-end filter of theinvention are described and claimed in applicants applications SerialNo. 203,595, Serial No. 203,596, and Serial No. 203,598, 10 filedconcurrently with the presentapplication while a general circuitarrangement, for maintaining a high impedance over a'wide frequencyrange across a pair of terminals having associated therewith inherentinductance tending to 18 limit the response of the system, is describedand broadly claimed in applicant's copending application Serial No;161,017, filed August 26, 1937, all assigned to the same asslgnee as thepresent application. 20

The novel features believed to be characteristic of the invention areset forth with particularity in theappe'nded claims. The inventionitself, however, both as to its organization and method of operation,together with further ob- 2c jects and advantages thereof, will best beunderstood by reference to the specification taken in connection withthe accompanying drawings, in which Fig. 1 is a simplified, orequivalent, circuit diagram utilized to explain the general theory ofthe invention; Fig. 2 is a graph-illustrating certain of the operatingcharacteristics of the circuit of Fig. 1; and each of Figs.3-10,inclusive, illustrates a different embodiment of a coupling circuitutilizingthe invention. as

The principles of the theoretical relations underlying the invention aredescribed most simply by reference to a nondissipative wave filter ofthe constant-k type. This filter may be fassumed to have an infinitenumber of sections or 40 to be terminatedwith its image impedance togive the same effect, The input impedance of such a filter is uniformover the pass bands if the input, termination is full-series orfull-shunt as distinguished from the usual mid-serieso'r 6 mid-shunttermination. The input impedance is the iterative impedance measured inseries with a full-series arm or in parallel with a full! shunt arm, asdistinguished from the conventional image impedance measured atmid-series so or mid-shunt. This input impedance may be regarded as atwo-terminal coupling impedance, the remainder of the filter servingmerely as a dead-end supplementary network utilized to secure thedesired uniform impedance. 5;

I ductance of the value l Any such filter f finite total band Width canbe arranged to include directiyacross its fullshunt arm, a capacitanceof the'value in whichR is the mid-band image impedance and A- is 2a'times the total widthof the pass bands.

The uniform full-shunt iterative impedance across the capacitance hasthe magnitude 7 V I r I a=2'/c s- (2) This relationship expresses thetheoretically maximum value of impedance thatcan be maintained acrossthe capacitance C throughout frequency bands of total width An." In thecase of a simple low-pass filter, the value of R is twice the reactanceof the capacitance C at the cutoff frequency.

The problem reciprocal to building up impedance across a shuntcapacitance is building up the admittance through an inductance.- Afilter can be arranged to include directly in series with all the otherelements ,of its series arm, an in- R' LAl/ V v This relationship Iexpresses the theoretically miiiimum value of impedance that can bemainanalogy which appears in the preceding formulae;

, The imageimpedance of a filter of the type under discussion is purelyresistive in the pass bands, though not uniform. On theother hand,the'uniform iterative impedance has a substanl m which n mm: mm mm asreferred t'othe impedance across a capacitance or'theladmittancethroughan inductance. The

phase characteristic is that of a half-section of a constant-k filter;

A more general analysis is given hereinafter with reference to a simplelow-pass filter, without anyloss of generality in the foregoingconcepts.

f Referring now to the-drawings, Fig. 1 shows the basic filter circuitinsimplified form, the filter beiniz representedschematically at'iandhavinginput termin als'l and output terminals I.

The input termination C-i'of'filter I isfa midshunt element and theinput image impedance Zi follows the constant-k characteristic. Theoutput termination of filter 'l. is either mid-series or mid-shunt anditsima'ge impedance Z prefer ably follows an rn-deri'ved characteristicto match closely the] output load resistance R0. In developing thetheoretical relations, this impedance matching is'assumedto be exactinthe pass 7 bands, since any of approximation is" possible by meansofmultiple m-derivations.

'l'br the sake of generality and clarity, the total capacitance C.across the input terminals I may have any value is divided in two parts,C- comprising the mid-shunt capacitance terminaion of the filter, andCn'the external added caimitat thu onl a part of the total c p cias amid-shunt element. therefore, across the total shunt. capacitance,

, y I 7 (a): I The uniformffuli-series iterative impedance through theinductance L has themagnitude time across terminals a is included in'thefilter The'impedance Z is,

C=C|i+Ca. This impedance is to be built up with the aid of a dead-endfilteracting merely as a passive auxiliary network.

The shunt capacitance Cm in the filter is the mid-shunt element ofa'terminal half-section. This half-section may be, of m-derived type(1n 1) or of constant-k type (1n=1)., since either type is available ina form whose mid-shunt termination presents the desired constant-k imageimpedance Zi across shunt capacitance Cm. In

-' such a half-section, the value ofthe mid-shunt capacitance is V cm=1nlRm (5) in which we is h/a'where is is the cutoff frequency of thelow-pass filter. The external shunt capacitance Cs can have any value asdetermined by the choice of the parameter win the formula,

. I Ca=1l/Roflc. (6)- Therefore, the total shunt capacitance isc.=c..+c.=f m+m new ('1) The factor (m+n) may have any positive value.One of the parts may be negative,since the parts dornot have to existseparately. Negative, Ca merely means that the total capacitance Co isless than the mid-shunt capacitance Cm of the filter. Equation (7) mayalso be written as The image impedance Z1 depends only on R and be, noton Cm and m, because it alwayshas the constant-k characteristic I Theimage impedance is resistive in the .pass band, capacitive in theattenuation band, and

infinite at the cutofffrequency. Itisconvenient to use the parameterz=u/w to denote the relative frequency in subsequent expressions. Therelative impedance of C- and Z1 in parallel is;

'1 (m e o/ l+j a o""7l1+jX n This formula has a discontinuity atthe'cutofi frequency (::=i), where the Zi term of the denominatorchanges from real. to imaginary. "It is seen that the form of theimpedance characteristic, depends only on from Equation (6 and does ,notdepend on I m=RsCm from Equation (5).

In the pass band (1K1), Z/Rs is complex and f n =1, this is constant;(unity). For greater 1 values of n, it has the form of a simple resistorand capacitor in parallel, though the phase angle is not the same. phaseangle. 7 V

' T 1 5 is the suns as the formula for a half-section The impedance hasalagging m-type filter except that the m of the filter is replaced bythe parameter n which determines the relative value of Cu. If n='1, itsimplifies to In the attenuation band (.1: 1), Z/Ro is imaginary and itsmagnitude is increases, this failure has less effect on the inputimpedance. Therefore, any degree of approximation to the theoreticalcharacteristics outside the pass band can be realized with a sufiicientnumber of sections designed to secure adequate attenuation.

Fig.2 shows the theoretical impedance characteristics for various valuesof the parameter a between -1 and +4. It is noted that the values :1yield uniform impedance in the pass band. If the filter has a constant-kwhole section on the input side, so that m=1, the values +1 and -l for ncorrespond, respectively, to full-shunt and full-series termination. Inthe former case, the addition of Co doubles the mid-shunt element, whilein the latter case it cancelsthe midshunt element. The sign of theparameter a does not affect the magnitude of the impedance in the passband, but it does determine the sign of the phase angle.

Since only positive self-reactance elements can be realized in a passivenetwork, the value of m in the end half-section of a filter must bebetween 0 and +1. Since m+n must be positive, the value of n must bebetween -1 and Negative values of n make the impedanceinfinite at thefrequency At higher frequencies, the phase angle is reversed in sign,b='-r/2.

Any of the impedance characteristics of Fig. 2 are theoreticallyobtainable across a maximum value of total shunt capacitance if m=d, nhaving the value identified with the characteristic curve. If m is lessthan one, the total capacitance directly across the input terminals isless by the amount added indirectly across the input terminals throughthe other arms of the filter. Therefore, a uniform impedance equal to R0in the pass band is obtainable across a maximum total capacitance,directly and indirectly in shunt, whose value is computed by letting1n=n=1z C'o=2/Roaic (20) which corresponds to Equation l. Any change ofthe total capacitance, by changing the value of 1!, causes an inversechange of the average impedance in the passband, although its value itsat zero frequency remains the same.

In the pass band, the impedance 'near the cutof! frequency is determinedmainly by the value of n, that is, by the external shunt capacitance On.The image impedance Z1 having less eifect, the tolerance of mismatchingbetween Zfland R0 at the far end of the'filter becomes greater. Also,this tolerance increases with n. The number of sections in the filteraffects the number of peaks and valleys in the actual, impedance curveof Z, while the phase characteristics affect their spacing along thefrequency axis.

Figs. 3- 10, inclusive, show several arrangements of low-pass filterschosen to illustrate the various degrees of complication and refinementand is provided with a terminating resistor Rs of such value as tomatch'the m-derived image impedance at the dead end of the filter overthe lowfrequency band. The parallel tuned circuit, which is a series armof "the m-derived section, is resonant slightly above the cutoflfrequency of the system, preferably between the limits of T/3 and /2times the cutofi' frequency.

The filter of Fig. 4 comprises a typical practical application of thefilter shown in Fig. 3 in which it is utilized as a coupling impedancebetween vacuum tubes I0 and II which may be amplifying tubes inalow-pass amplifier designed to amplify a wide band of frequencies. Thetotal inherent capacitance of the output circuit of vacuum tube II andthe input circuit of vacuum tube H is represented by the condenser l2.shown in V dotted lines. All the elements of the filter of Fig. 3 arepresent in the filter of Fig. 4, the condenser I! having a capacitanceequal to the total capacitance of condensers Cu and Cm of Fig. 3. Inthecircuit of Fig. 4, the position of terminating resistor R0 and theparallel-connected inductance and capacitance elements of the mderivedsection of the filter of Fig. 3 have been ticular systems. In Fig.5-there is shown a deadend filter of the invention comprising, in theorder named, external condenser Cs, a constant-k half-section of whichthe condenser Cu is a midshunt element, an m-derived half-sectionindicated at m in the drawings, 'and'terminating resistor R0 theimpedance of which matches the image impedance of the m-derived sectionat the dead end of the filter overthe pass band.

In' Fig. 8 there is shown a filterof the invention comprising, in theorder named, external condenser Cn, a constant-k whole section of whichthe condenser Cm is a mid-shunt element. an m-derived half-sectionindicated at m in the drawings, and a terminating resistor R the iresistance of which matches the image impedance of the m-derived filtersection over the pass band. i

p The filter of Fig. l is in all respects equivalent to that shown lung.6 and is utilized as a coupling impedance between vacuum tubes "and 2|which may comprise tubes of a low-pass am: plifier for amplifying a wideband rat-frequencies. The elements C and Cu have been combined in thefilter of Fig. 7 as the capacitance represented by condenser 22 shown indotted lines.

Condenser 22 may be comprised in whole or in inherent capacitance of thepartof the total flandtheinputcircuitof output circuit of tube tube 1|.Adjacent elements of'simiiar kind of the circuit of Fig. 6 havebeencombined into one element in the circuit of Fig. 7. The position oiterminating resistor'Ro andthe parallel inductance-capacitance circuitof the m-derived section of Fig. 6 have been reversed, thesparallelinductance-capacitance circuit being denoted 23 in Fig. 7-. A grid leak24 is provided for v acuum tube 2| which mayhave an appreciable effectupon the operation of the filter circuit shown. It will beunderstoodthat the effect of this resistor upon the operation of the filter can be'takeninto consideration in the design of the filter elements in themanner described in detail in the above-mentioned copending application,Serial No. 203,595.

In Fig; 8 there is shown a dead-end filter com- .prising, in the ordernamed, external condenser Cu, an" m-derived half-section indicated at min the drawings of which condenser Cm is a midshuntelement, a doublem-derived half-section indicated atm' in the drawings, and aterminatingresistor R the resistance of which matches the image resistance of thedead-end filter very closely over the pass band, and exactlyat threefrequencies in theband.

t "The filter of Fig. 9 comprises, in the order named, externalcondenser Cu, a constant k haltsection of which Cm is the mid-shuntelement,

an 'm-derivedhalt-section indicated at m in the drawings, a doublem-derived half-section indicated at m',,m" in the drawings, andterminatingv resistor R0; the resistance of which matches the imageimpedance of the filter over thepassband.

The filter 01' Fig. 10 comprises, in the order named-external condenserCa, a constant-k section of which condenser Cm is a mid-shunt element,-an m-derlved halt-section indicated at m in the drawings, a doublem-derived haltsection indicated, atm. mf' in the drawings, and

terminating resistorm the resistance oi which matches the imageimpedance oi thefilter over the passband.

It will beseenthat the filters of Figs. 5, 6,7, 9.,and 10 have theirentire external-capacitance in shunt across the input terminals, thatis,

' m=1 in the mid-shunt, arm comprising Cu.

These filters can be practically realized only if the inductanceelements of the filter can be made with negligible shunt capacitance.Otherwise, the filters oi Hgs. 3, 4, and 8 can be utilized, whichtolerate about 20% less shunt capacitance (m=0.6), in. addition to thatacross the inductance elements. It will also be notedthat, in thefilters 01. Figs. and 7,.the capacitance to ground from every junctionpoint of the filter is includedin the filter design. The filters of A 7some of the'otherfigures. also can be arranged to secure this advantage.In the design of. the .dead-end'filters of the invention, .the preferredvalue "01' m in themderived sections is of the order of 0.6. Values ofmbetween the limits of 0.5to 0.7 result in "a matching of the imageimpedance of the mderived filter section with (the terminating resistorR0 at two points-in the low-pass band. Filters having an m-derivedtermination with a value of m more than 0.7 cannot match the terminalresistor Beat more than one point in the low-pass band. Eachadditionalm-deriva- .tion includedin the filter. termination makesit possibletomatchthe' image impedance" with the terminal resistor at one additionalpoint in the low-pass band.

While there have been described what are at t present considered to bethe preferred. embodito the input and output circuits of said system andacross which there is effectively capacitance tending to limit theresponse of said system over said range, a dead-end filter having'apredetermined image impedance over said range coupled to said terminals,said filter comprising only a part of, said capacitance as a terminalmid-shunt element, and an impedance termination coupled to the dead endof said filter proportioned substantially to match the image impedanceof said filter over said range, the reactive constants of said dead-endfilter being-so proportioned relative to said capacitance and theoperating frequency-range that the mean-value of theimpedance acrosssaid terminals over said range is "approximately the maximum that can be'maintained over said range.-

2. A low-pass two-terminal signal-translating system for operation over'a wide range 01'. Irecapacitance across said terminalstending to limitthe requencies comprising substantial sponse' of said system over saidrange, a deadend filterhaving apredetermined image impedance over saidrange coupled to said terminals, 1 said filter comprising only a part ofsaid capac ltance as a terminal mid-shunt element, an

m-derived impedance termination coupled to the.

"dead end of said filter, a'terminating resistor coupled to saidimpedance. termination, saidimpedance termination being proportionedsubstantially to match the imageimpedance oi said filter to saidresistor over said range and exactly to match the image impedance ofsaid filter to said resistor at two points in said range, the reactiveconstantsof. said dead-end-filter being so proportioned relative to saidcapacitance and the operating frequency range that the impedance across.said terminals oversaid range is substantially uniform and the maximumthat can be maintained thereacross over said 3 range.

. 3. A high-frequency ampliiying systemfor operation over a wide rangeof frequencies comprising two vacuum-tube amplifiers having input andoutput terminals one of said tubes having appreciable output capacitanceand the other of said tubes having appreciable input capacitance, saidcapacitances'being eflectively in parallel and tending to limit theresponse 01 said, system' over' said range, a dead-end filter having apredetermined image impedance over said range; and.

comprising only apart of said capacitances as a terminal mid-shuntelement,an m-derived im-. pedance termination coupled to the dead-end ofsaid filter, a'terminating resistor coupled to said impedancetermination," said impedance termination being proportionedsubstantially to match the image impedance 01' said filter over said.range and exactly tomatch the image impedance pf said filter at twopoints in said range,the reactive constants or said dead-end filterbeing so V proportioned relative to said capacitances and arouse 4. Alow-pass two-terminal signal--i :ranslating system for operation over awide range of frequencies comprising substantial capacitance across saidterminals tending, to limit the response of said system over said range,a deadend filter having a, predetermined image imped-' ance over saidrange coupled to said terminals and comprising only a part of saidcapacitance as a terminal mid-shunt element, an m-deriyed impedancetermination in said filter comprising a parallel-resonant circuit as aseries arm, a terminal resistor coupled to said impedance termination,said impedance termination being proportioned substantially to match theimage impedance of said filter with said resistor over said range, thereactive constants of said dead-end filter being so proportionedrelative to said capacitance and the operating range that the impedanceacross said terminals over said range is substantially uniform andapproximately the maximum that can be maintained across said terminalsover said range.

5. A low-pass two-terminal signal-translating system for operation overa wide'range of fre-, quencies comprising substantial capacitance acrosssaid terminals tending to limit the response of said system over saidrange, a deadend filter having a predetermined image impedance over saidrange coupledto said terminals and comprising only a part of saidcapacitance as a terminal mid-shuntjelement, an m-derived impedancetermination in said filter comprisin a parallel-resonant circuit as aseries arm, said parallel-resonant circuit tuned between the limits of Ination, said impedance termination being proportioned to match the imageimpedance of said filter with said resistor over said range, thereactiveconstants of said dead-end filter belng'so proportioned relative to saidcapacitance and the operating range that the impedance across saidterminals over said range is substantially uniform and approximately.the maximum maintained across said terminalsoyeri'said range.

6. A low-pass two-terminalsignal translating system for operation over.a offrequencies comprising substantial sa-id terminals tending toWhit-laidsystem over saidrange, a a predetermined image Y impedance,foyer. said range coupledto said terminals only a part of saidcapacitance as a shunt element, an m-derived impedance termination forsaid filter comprising a'parailel-resonant circuit as a series arm, saidparallel-resonant circuit being resonant slightly above the cut oiffrequency, a terminal resistor coupled tosaid impedance termination,said impedance termi-v nation being proportioned substantially to matchsistor over said range, the reactive constants of terminals over saidrange. v '7. A low-pass two-terminal signal-translating system foroperation over a wide range of frequencies comprising "substantialcapacitance the maximum that can be maintained across said across saidterminals tending to limit the response of said system-over said range,a dead-end filter having a predetermined image impedance over said rangecoupled to said terminals, said filter comprising only a part of saidcapacitance as a" terminal mid-shunt element,'anim-derived impedancetermination including a series-resonant shunt arm in said dead-endfilter, a terminal re-' sister coupled to said impedance termination,said impedance termination being proportioned substantialiyto match theimage impedance of said filter with said resistor over said range, thereactive constants of said filter being so proper tioned relative tosaid capacitance and the operating frequency range that the impedanceacross said pair of terminals over said range is substantially uniformand approximately the maximum that can be maintained over range.

8. A high-frequency amplifying system for operation over a wide range offrequencies comprising two vacuum tubes having input and outputterminals, one of said vacuum tubes having e appreciable outputcapacitance and the other of said vacuum tubes having appreciable inputcapacitance, said capacitances being effectively in parallel and tendingto limit the response of said amplifier over said range, a dead-endfilter efiectively comprising a constant-k whole section having apredetermined image impedance over said range and including only a partof said capacitances as a terminal mid-shunt element, an m-derlvedimpedance termination effectively comprising a parallel-resonant circuitas a series arm and coupled to the dead end of said filter, a terminalresistor for said impedance termination, said impedance terminationbeing proportioned substantially to match the impedance system foroperation over a wide range of frequencies comprising substantialcapacitance across said terminals tending to limit the response of saidsystem over said range, a deadance over said range coupled to saidterminals and [comprising only a part of said capacitance as a terminalmid-shunt element, an m-derived impedance termination having a value ofm of the -'-;order of 0.6 coupled to the dead end of said filter,

a terminal resistor for said impedance termination, said impedancetermination being proportioned substantially to match the imageimpedance of said filter'with said resistor over said range, thereactiveconstants of said filter being so proportioned relative to saidcapacitance and the operating frequency range that the impedance theimage impedance of said filter with said re-v across said terminals oversaidrange is substantiallyuniform and approximately the maximum thatmaintained thereacroes over said 5 '10. A two-terminal low-passsignal-translating 1k system'for operation over a'wide range of freendfilter having a predetermined image impedquencies comprisingsubstantial. capacitance acrosssaid terminals tending to limit theresponse oi! saidsystem over said range, a deadend filter having apredetermined image impedance over said range coupled to'said terminals,said filter comprising only a part 01' said capacitance as' a terminalmid-elemenhan mderived impedance termination having a value of m between0.5 and 0.7 coupled to the dead end of said filter, a terminal resistorfor said impedance termination, said impedance termination V 2,1e7,1ao'V J being proportioned substantially to inatch the imageimpedance o!saidfllter with said resistor over said range, the reactive constants oisaid dead-end filter being so proportioned relative to said capacitanceand the operating frequency range that the impedance across saidterminals over said range is substantially uniform and approximately themaximum that can be maintained thereacrcss over said range.

,HAROLD A, :lum 0o-

